ELLIPTIC EQUATIONS WITH ABSORPTION IN A HALF-SPACE

Jorge García-Melián (1) , A Quaas (1) , B Sirakov (2)

1 Departamento de Matematica [Valparaiso]
2 Departamento de Matematica

We give a necessary and sufficient condition, in the spirit of the clas-sical works by Keller and Osserman, for the elliptic equation ∆u = f (u) to have a solution in a half-space of R N . The function f is supposed to be nondecreasing and nonnegative, and we are interested in solutions whose range is where f > 0.

Domaines: Equations aux dérivées partielles [math.AP]

Jorge García-Melián, A Quaas, B Sirakov. ELLIPTIC EQUATIONS WITH ABSORPTION IN A HALF-SPACE. 2015. ⟨hal-01111679v2⟩